Idea of Bowler Hat Icon
It is a hat, much like a derby hat. The hat itself has a mostly rounded crown, although it does appear to be slightly flattened. The sides of the hat extend straight down from the rounded crown onto the brim, which is fairly narrow and close in to the crown. The brim curls up slightly at the sides.
This page shows the different variations of the Bowler Hat from an Icons8 icon pack. Feel free to resize and recolor the icon, and then download the icon in PNG format for free.